And the archetypal numbers, which are the models of these three are, of the point the limit, of the line the number two, and of the superficies the number three, and of the solid the number four; the combination of which, that is to say of one, and two, and three, and four completes the decade, which displays other beauties also in addition to those which are visible.


 For one may almost say that the whole infinity of


 


 numbers is measured by this one, because the boundaries which make it up are four, namely, one, two, three, and four; and an equal number of boundaries, corresponding to them in equal proportions, make up the number of a hundred out of decades; for ten, and twenty, and thirty, and forty produce a hundred. And in the same way one may produce the number of a thousand from hundreds, and that of a myriad from thousands. And the unit, and the decade, and the century, and the thousand, are the four boundaries which generate the decade, which last number, besides what has been already said, displays also other differences of numbers, both the first, which is measured by the unit alone, of which an instance is found in the numbers three, or five, or seven; and the square which is the fourth power, which is an equally equal number. Also the cube, which is the eighth power, which is equally equal equally, and also the perfect number, the number six, which is made equal to its component parts, three, and two, and one.


 But what is the use now of enumerating the excellencies of the decade, which are infinite in number; treating our most important task as one of no importance, which is, indeed, of itself most all-sufficient, and worthy material for the study of those who devote themselves to mathematics?


The other points we must pass over for the present; but perhaps it may not be out of place to mention one by way of example; for those who have devoted themselves to the doctrines of philosophy say that what are called the categories in nature are ten only in number, —quality, essence, quantity, relation, action, passion, possession, condition, and those two without which nothing can exist, time and place.